Question

Determine the equivalent system for the given system of equations.4x − 5y = 23x − y = 8

Answer 1

Given:

`\begin{gathered} 4x-5y=2 \\ 3x-y=8 \end{gathered}`

Two systems of equations are equivalent if they have exactly the same solution set.

Hence, we determine the solution to the system of equations.

`\begin{gathered} 4x-5y=2\ldots\ldots.\ldots.\ldots.\ldots.(1) \\ 3x-y=8\ldots\ldots.\ldots\ldots\ldots\ldots..(2) \\ \\ m\text{ ultiplying equation (2) by 5} \\ 5(3x-y)=5(8) \\ 15x-5y=40 \\ \\ \text{Solving both equations (1) and the newly formed equation (2) simultaneously,} \\ 4x-5y=2\ldots\ldots\ldots\ldots(1) \\ 15x-5y=40\ldots\ldots\ldots.\mathrm{}(2) \end{gathered}`

Subtracting equation (1) from equation (2),

Equation (2) - equation (1) becomes;